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This study investigates the potential impact of climate change on residual contaminants in vadose zones and groundwater. We assume that the effect of climate changes can be represented by perturbations in the natural recharge through the aquifer system. We perform numerical modeling of unsaturated/saturated flow and transport and consider different performance metrics: contaminant concentrations at observation wells and contaminant export at the site's boundary. We evaluate the effect of increasing and decreasing recharge as well as the impact of potential failure of surface capping structures employed to immobilize vadose zone contaminants. Our approach is demonstrated in a real case study by simulating transport of non-reactive radioactive tritium at the U.S. Department of Energy's Savannah River Site. Results show that recharge changes significantly affect well concentrations: after an initial slight dilution we identify a significant concentration increase at different observation wells some years after the recharge increase and/or the cap failure, as a consequence of contaminants' mobilization. This effect is generally emphasized and occurs earlier as the recharge increases. Under decreased aquifers' recharge the concentration could slightly increase for some years, due to a decrease of dilution, depending on the magnitude of the negative recharge shift. We identify trigger levels of recharge above which the concentration/export breakthrough curves and the time of exceedance of the Maximum Contaminant Level for tritium are remarkably affected. Moreover, we observe that the contaminant export at the control plane, identified as the risk pathway to the downgradient population, may only be minimally affected by shifts in the natural recharge regime, except for some extreme cases. We conclude that more frequent sampling and in-situ monitoring near the source zone should be adopted to better explain concentrations' anomalies under changing climatic conditions. Moreover, the maintenance of the cap is critical not only to sequester residual contaminants in the vadose zone, but also to reduce the uncertainty associated with future precipitation changes. Finally, realistic flow and transport simulations achieved through proper calibration processes, rather than conservative modeling, should be adopted to identify non-trivial trade-offs which enable better allocation of resources towards reducing uncertainty in decision making.